Free energy approximations in simple lattice proteins

This work addresses the question of whether it is possible to define simple pairwise interaction terms to approximate free energies of proteins or polymers. Rather than ask how reliable a potential of mean force is, one can ask how reliable it could possibly be. In a two-dimensional, infinite lattice model system one can calculate exact free energies by exhaustive enumeration. A series of approximations were fitted to exact results to assess the feasibility and utility of pairwise free energy terms. Approximating the true free energy with pairwise interactions gives a poor fit with little transferability between systems of different size. Adding extra artificial terms to the approximation yields better fits, but does not improve the ability to generalize from one system size to another. Furthermore, one cannot distinguish folding from nonfolding sequences via the approximated free energies. Most usefully, the methodology shows how one can assess the utility of various terms in lattice protein/polymer models. (C) 2001 American Institute of Physics.

Tuning the metal-to-metal charge transfer energy of cyano-bridged dinuclear complexes

The metal-to-metal charge transfer (MMCT) transitions of a series of Class II mixed valence dinuclear complexes bearing cyano bridging ligands may be varied systematically by variations to either the hexacyanometallate(II) donor or Co-III acceptor moieties. Specifically, the new dinuclear species trans-[(LCoNCFe)-Co-14S(CN)(5)](-) (L-14S = 6-methyl-1,11-diaza-4,8-dithia- cyclotetradecane-6-amine) and trans-[(LCoNCRu)-Co-14(CN)(5)]-(L-14 = 6-methyl-1,4,8,11-tetraazacyclotetradecane-6-amine) have been prepared and their spectroscopic and electrochemical properties are compared with the relative trans-[(LCoNCFe)-Co-14(CN)(5)](-). The crystal structures of Na{trans-[(LCoNCFe)-Co-14S(CN)(5)]}.51/2H(2)O.1/2EtOH, Na{trans-[(LCoNCRu)-Co-14(CN)(5)]}.3H(2)O and Na{trans-[(LCoNCRu)-Co-14(CN)(5)]}.8H(2)O are also reported. The ensuing changes to the MMCT energy have been examined within the framework of Hush theory, and it was found that the free energy change between the redox isomers was the dominant effect in altering the energy of the MMCT transition.

In vivo protein cyclization promoted by a circularly permuted Synechocystis sp PCC6803 DnaB mini-intein

A synthetic Synechocystis sp. PCC6803 DnaB split mini-intein gene was constructed for the in vivo cyclization of recombinant proteins expressed in Escherichia coli. The system was used to cyclize the NH2-terminal domain of E. coli DnaB, the structure of which had been determined previously by NMR spectroscopy. Cyclization was found to proceed efficiently, with little accumulation of precursor, and the product was purified in high yield. The solution structure of cyclic DnaB-N is not significantly different from that of linear DnaB-N and it unfolds reversibly at temperatures similar to14 degreesC higher. Improved hydrogen bonding was observed in the first and last helices, and the length of the last helix was increased, while the 9-amino acid linker used to join the NH2 and COOH termini was found to be highly mobile. The measured thermodynamic stabilization of the structure (DeltaDeltaG approximate to 2 kcal/mol) agrees well with the value estimated from the reduced conformational entropy in the unfolded form. Simple polymer theory can be used to predict likely free energy changes resulting from protein cyclization and how the stabilization depends on the size of the protein and the length of the linker used to connect the termini.

Stabilization of native protein fold by intein-mediated covalent cyclization

A mutant version of the N-terminal domain of Escherichia coli DnaB helicase was used as a model system to assess the stabilization against unfolding gained by covalent cyclization. Cyclization was achieved in vivo by formation of an amide bond between the N and C termini with the help of a split mini-intein. Linear and circular proteins were constructed to be identical in amino acid sequence. Mutagenesis of Phe102 to Glu rendered the protein monomeric even at high concentration. A difference in free energy of unfolding, DeltaDeltaG, between circular and linear protein of 2.3(+/-0.5) kcal mol(-1) was measured at 10degreesC by circular dichroism. A theoretical estimate of the difference in conformational entropy of linear and circular random chains in a three-dimensional cubic lattice model predicted DeltaDeltaG = 2.3 kcal mol(-1), suggesting that stabilization by protein cyclization is driven by the reduced conformational entropy of the unfolded state. Amide-proton exchange rates measured by NMR spectroscopy and mass spectrometry showed a uniform, approximately tenfold decrease of the exchange rates of the most slowly exchanging amide protons, demonstrating that cyclization globally decreases the unfolding rate of the protein. The amide proton exchange was found to follow EX1 kinetics at near-neutral pH, in agreement with an unusually slow refolding I measured by stopped-flow circular dichroism. rate of less than 4 min(-1) The linear and circular proteins differed more in their unfolding than in their folding rates. Global unfolding of the N-terminal domain of E. coli DnaB is thus promoted strongly by spatial separation of the N and C termini, whereas their proximity is much less important for folding. (C) 2005 Elsevier Ltd. All rights reserved.

Effects of molecular crowding by saccharides on alpha-chymotrypsin dimerization

Given the importance of protein complexes as therapeutic targets, it is necessary to understand the physical chemistry of these interactions under the crowded conditions that exist in cells. We have used sedimentation equilibrium to quantify the enhancement of the reversible homodimerization of alpha-chymotrypsin by high concentrations of the osmolytes glucose, sucrose, and raffinose. In an attempt to rationalize the ostuolyte-mediated stabilization of the a-chymotrypsin homodimer, we have used models based on binding interactions (transfer-free energy analysis) and steric interactions (excluded volume theory) to predict the stabilization. Although transfer-free energy analysis predicts reasonably well the relatively small stabilization observed for complex formation between cytochrome c and cytochrome c peroxidase, as well as that between bobtail quail lysozyme and a monoclonal Fab fragment, it underestimates the sugar-mediated stabilization of the alpha-chymotrypsin dimer. Although predictions based on excluded volume theory overestimate the stabilization, it would seem that a major determinant in the observed stabilization of the a-chymotrypsin homodimer is the thermodynamic nonideality arising from molecular crowding by the three small sugars.

Factors affecting the rate of phosphocreatine resynthesis following intense exercise

Within the skeletal muscle cell at the onset of muscular contraction, phosphocreatine (PCr) represents the most immediate reserve for the rephosphorylation of adenosine triphosphate (ATP). As a result, its concentration can be reduced to less than 30% of resting levels during intense exercise. As a fall in the level of PCr appears to adversely affect muscle contraction, and therefore power output in a subsequent bout, maximising the rate of PCr resynthesis during a brief recovery period will be of benefit to an athlete involved in activities which demand intermittent exercise. Although this resynthesis process simply involves the rephosphorylation of creatine by aerobically produced ATP (with the release of protons), it has both a fast and slow component, each proceeding at a rate that is controlled by different components of the creatine kinase equilibrium. The initial fast phase appears to proceed at a rate independent of muscle pH. Instead, its rate appears to be controlled by adenosine diphosphate (ADP) levels; either directly through its free cytosolic concentration, or indirectly, through its effect on the free energy of ATP hydrolysis. Once this fast phase of recovery is complete, there is a secondary slower phase that appears almost certainly rate-dependant on the return of the muscle cell to homeostatic intracellular pH. Given the importance of oxidative phosphorylation in this resynthesis process, those individuals with an elevated aerobic power should be able to resynthesise PCr at a more rapid rate than their sedentary counterparts. However, results from studies that have used phosphorus nuclear magnetic resonance (P-31-NMR) spectroscopy, have been somewhat inconsistent with respect to the relationship between aerobic power and PCr recovery following intense exercise. Because of the methodological constraints that appear to have limited a number of these studies, further research in this area is warranted.

Modeling of phase equilibrium and vapor adsorption on carbon black based on a combination of a lattice theory and equation of state

A thermodynamic approach is developed in this paper to describe the behavior of a subcritical fluid in the neighborhood of vapor-liquid interface and close to a graphite surface. The fluid is modeled as a system of parallel molecular layers. The Helmholtz free energy of the fluid is expressed as the sum of the intrinsic Helmholtz free energies of separate layers and the potential energy of their mutual interactions calculated by the 10-4 potential. This Helmholtz free energy is described by an equation of state (such as the Bender or Peng-Robinson equation), which allows us a convenient means to obtain the intrinsic Helmholtz free energy of each molecular layer as a function of its two-dimensional density. All molecular layers of the bulk fluid are in mechanical equilibrium corresponding to the minimum of the total potential energy. In the case of adsorption the external potential exerted by the graphite layers is added to the free energy. The state of the interface zone between the liquid and the vapor phases or the state of the adsorbed phase is determined by the minimum of the grand potential. In the case of phase equilibrium the approach leads to the distribution of density and pressure over the transition zone. The interrelation between the collision diameter and the potential well depth was determined by the surface tension. It was shown that the distance between neighboring molecular layers substantially changes in the vapor-liquid transition zone and in the adsorbed phase with loading. The approach is considered in this paper for the case of adsorption of argon and nitrogen on carbon black. In both cases an excellent agreement with the experimental data was achieved without additional assumptions and fitting parameters, except for the fluid-solid potential well depth. The approach has far-reaching consequences and can be readily extended to the model of adsorption in slit pores of carbonaceous materials and to the analysis of multicomponent adsorption systems. (C) 2002 Elsevier Science (USA).

Adsorption in slit-like pores of activated carbons: Improvement of the Horvath and Kawazoe method

Anew thermodynamic approach has been developed in this paper to analyze adsorption in slitlike pores. The equilibrium is described by two thermodynamic conditions: the Helmholtz free energy must be minimal, and the grand potential functional at that minimum must be negative. This approach has led to local isotherms that describe adsorption in the form of a single layer or two layers near the pore walls. In narrow pores local isotherms have one step that could be either very sharp but continuous or discontinuous benchlike for a definite range of pore width. The latter reflects a so-called 0 --> 1 monolayer transition. In relatively wide pores, local isotherms have two steps, of which the first step corresponds to the appearance of two layers near the pore walls, while the second step corresponds to the filling of the space between these layers. All features of local isotherms are in agreement with the results obtained from the density functional theory and Monte Carlo simulations. The approach is used for determining pore size distributions of carbon materials. We illustrate this with the benzene adsorption data on activated carbon at 20, 50, and 80 degreesC, argon adsorption on activated carbon Norit ROX at 87.3 K, and nitrogen adsorption on activated carbon Norit R1 at 77.3 K.

Mixed gas equilibrium adsorption on zeolites and energetic heterogeneity of adsorption volume

A model for binary mixture adsorption accounting for energetic heterogeneity and intermolecular interactions is proposed in this paper. The model is based on statistical thermodynamics, and it is able to describe molecular rearrangement of a mixture in a nonuniform adsorption field inside a cavity. The Helmholtz free energy obtained in the framework of this approach has upper and lower limits, which define a permissible range in which all possible solutions will be found. One limit corresponds to a completely chaotic distribution of molecules within a cavity, while the other corresponds to a maximum ordered molecular structure. Comparison of the nearly ideal O-2-N-2-zeolite NaX system at ambient temperature with the system Of O-2-N-2-zeolite CaX at 144 K has shown that a decrease of temperature leads to a molecular rearrangement in the cavity volume, which results from the difference in the fluid-solid interactions. The model is able to describe this behavior and therefore allows predicting mixture adsorption more accurately compared to those assuming energetic uniformity of the adsorption volume. Another feature of the model is its ability to correctly describe the negative deviations from Raoult's law exhibited by the O-2-N-2-CaX system at 144 K. Analysis of the highly nonideal CO2-C2H6-zeolite NaX system has shown that the spatial molecular rearrangement in separate cavities is induced by not only the ion-quadrupole interaction of the CO2 molecule but also the significant difference in molecular size and the difference between the intermolecular interactions of molecules of the same species and those of molecules of different species. This leads to the highly ordered structure of this system.

Phase equilibria and surface tension of pure fluids using a molecular layer structure theory (MLST) model

This paper presents a new model based on thermodynamic and molecular interaction between molecules to describe the vapour-liquid phase equilibria and surface tension of pure component. The model assumes that the bulk fluid can be characterised as set of parallel layers. Because of this molecular structure, we coin the model as the molecular layer structure theory (MLST). Each layer has two energetic components. One is the interaction energy of one molecule of that layer with all surrounding layers. The other component is the intra-layer Helmholtz free energy, which accounts for the internal energy and the entropy of that layer. The equilibrium between two separating phases is derived from the minimum of the grand potential, and the surface tension is calculated as the excess of the Helmholtz energy of the system. We test this model with a number of components, argon, krypton, ethane, n-butane, iso-butane, ethylene and sulphur hexafluoride, and the results are very satisfactory. (C) 2002 Elsevier Science B.V. All rights reserved.

Mechanical alloying of MoSi2 with ternary alloying elements. Part 2 - computer simulation

A computer model of the mechanical alloying process has been developed to simulate phase formation during the mechanical alloying of Mo and Si elemental powders with a ternary addition of Al, Mg, Ti or Zr. Using the Arhennius equation, the model balances the formation rates of the competing reactions that are observed during milling. These reactions include the formation of tetragonal C11(b) MOSi2 (t-MoSi2) by combustion, the formation of the hexagonal C40 MoSi2 polymorph (h-MoSi2), the transformation of the tetragonal to the hexagonal form, and the recovery of t-MoSi2 from h-MoSi2 and deformed t-MoSi2. The addition of the ternary additions changes the free energy of formation of the associated MoSi2 alloys, i.e. Mo(Si, Al)(2), Mo(Mg, Al)(2), (Mo, Ti)Si-2 (Mo, Zr)Si-2 and (Mo, Fe)Si-2, respectively. Variation of the energy of formation alone is sufficient for the simulation to accurately model the observed phase formation. (C) 2003 Elsevier B.V. All rights reserved.

Application of density functional theory to equilibrium adsorption of argon and nitrogen on amorphous silica surface

We present a new version of non-local density functional theory (NL-DFT) adapted to description of vapor adsorption isotherms on amorphous materials like non-porous silica. The novel feature of this approach is that it accounts for the roughness of adsorbent surface. The solid–fluid interaction is described in the same framework as in the case of fluid–fluid interactions, using the Weeks–Chandler–Andersen (WCA) scheme and the Carnahan–Starling (CS) equation for attractive and repulsive parts of the Helmholtz free energy, respectively. Application to nitrogen and argon adsorption isotherms on non-porous silica LiChrospher Si-1000 at their boiling points, recently published by Jaroniec and co-workers, has shown an excellent correlative ability of our approach over the complete range of pressures, which suggests that the surface roughness is mostly the reason for the observed behavior of adsorption isotherms. From the analysis of these data, we found that in the case of nitrogen adsorption short-range interactions between oxygen atoms on the silica surface and quadrupole of nitrogen molecules play an important role. The approach presented in this paper may be further used in quantitative analysis of adsorption and desorption isotherms in cylindrical pores such as MCM-41 and carbon nanotubes.

Adsorption of N-2, Ar, acetone, chloroform and acetone-chloroform mixture on carbon black in the framework of molecular layer structure theory (MLST)

Adsorption of pure nitrogen, argon, acetone, chloroform and acetone-chloroform mixture on graphitized thermal carbon black is considered at sub-critical conditions by means of molecular layer structure theory (MLST). In the present version of the MLST an adsorbed fluid is considered as a sequence of 2D molecular layers, whose Helmholtz free energies are obtained directly from the analysis of experimental adsorption isotherm of pure components. The interaction of the nearest layers is accounted for in the framework of mean field approximation. This approach allows quantitative correlating of experimental nitrogen and argon adsorption isotherm both in the monolayer region and in the range of multi-layer coverage up to 10 molecular layers. In the case of acetone and chloroform the approach also leads to excellent quantitative correlation of adsorption isotherms, while molecular approaches such as the non-local density functional theory (NLDFT) fail to describe those isotherms. We extend our new method to calculate the Helmholtz free energy of an adsorbed mixture using a simple mixing rule, and this allows us to predict mixture adsorption isotherms from pure component adsorption isotherms. The approach, which accounts for the difference in composition in different molecular layers, is tested against the experimental data of acetone-chloroform mixture (non-ideal mixture) adsorption on graphitized thermal carbon black at 50 degrees C. (C) 2005 Elsevier Ltd. All rights reserved.

The effects of parabens on the mechanosensitive channels of E. coli

Parabens are alkyl esters of p-hydroxybenzoic acid used as preservatives in a wide range of food, pharmaceutical, and cosmetic products (Soni et al. Food Chem. Toxicol. 39:513-532, 2001). Despite their common use for over 50 years, their mechanism of action is still unclear. In this study we examined the effects of ethyl and propyl paraben, on gating of the E. coli mechanosensitive channel of large conductance (MscL) reconstituted into azolectin liposomes. We found that propyl and ethyl paraben spontaneously activate MscL. Moreover, the addition of propyl paraben caused an increase in MscL activity and the lowering Of P-1/2, the pressure at which the MscL was opened 50% of the time, the AGO, the free energy required to open the MscL, and the parameter a, which describes the channel sensitivity to pressure. In addition, in silico studies showed that propyl paraben binds to the channel gate of the MscL. The mechanosensitive channel of small conductance was also found to be spontaneously activated by parabens. In summary, our study indicates that one of the previously unidentified mechanisms of action of parabens as antimicrobial agents is via an interaction with the mechanosensitive channels to upset the osmotic gradients in bacteria.

Modeling of adsorption and nucleation in infinite cylindrical pores by two-dimensional density functional theory

In this paper, we present an analysis of argon adsorption in cylindrical pores having amorphous silica structure by means of a nonlocal density functional theory (NLDFT). In the modeling, we account for the radial and longitudinal density distributions, which allow us to consider the interface between the liquidlike and vaporlike fluids separated by a hemispherical meniscus in the canonical ensemble. The Helmholtz free energy of the meniscus was determined as a function of pore diameter. The canonical NLDFT simulations show the details of density rearrangement at the vaporlike and liquidlike spinodal points. The limits of stability of the smallest bridge and the smallest bubble were also determined with the canonical NLDFT. The energy of nucleation as a function of the bulk pressure and the pore diameter was determined with the grand canonical NLDFT using an additional external potential field. It was shown that the experimentally observed reversibility of argon adsorption isotherms at its boiling point up to the pore diameter of 4 nm is possible if the potential barrier of 22kT is overcome due to density fluctuations.